Our previous analysis [1]}, using calculated SDCs,
addressed the production of the \(\psi {\rm (2S)}\)  and \(\Upsilon {\rm (3S)}\)  quarkonia,
the ones less affected by feed-down decays from P-wave quarkonia.
We now concentrate on the charmonium system, complementing the \(\psi {\rm (2S)}\)  measurements with \({\rm J}/\psi \) , \(\chi _{c1}\)  and \(\chi _{c2}\)  data.
The bottomonium system, with its more articulated feed-down structure, not yet sufficiently constrained by data
(no mid-rapidity \(\chi _{b}\)  measurements exist), is left for future consideration.
We also profit from much improved \(\psi {\rm (2S)}\)  and \({\rm J}/\psi \)  cross section measurements recently made available by ATLAS and CMS,
extending to significantly higher \(p_{\rm T}\) .
The similarity of the \(p_{\rm T}/M\)  dependencies shown by these precise measurements,
discussed in Section ,
guides us to assuming that the direct production mechanism is the same for the \({\rm J}/\psi \)  and \(\psi {\rm (2S)}\)  mesons.
This translates, in our fit, in the use of a single “polarized fraction”, represented by the parameter \(f_{\rm p}^{*}\) , common to the two states.
